Join the two tables to filter on the date:

INSERT INTO DB_Archive.dbo.Prescription_D

SELECT Prescription_D.*

FROM Prescription_D

INNER JOIN Prescription_H

ON Prescription_D.Presc_No = Prescription_H.Presc_No

WHERE Prescription_H.Modify_Dt >= CONVERT(DATETIME, '01-01-2010', 103)and Prescription_H.Modify_Dt <= CONVERT(DATETIME, '01-01-2011', 103)

INSERT INTO DB_Archive.dbo.Prescription_H

SELECT *

FROM Prescription_H

WHERE Modify_Dt >= CONVERT(DATETIME, '01-01-2010', 103)and Modify_Dt <= CONVERT(DATETIME, '01-01-2011', 103)